# Research Seminars

## Partially Observable Risk-Sensitive Markov Decision Processes

Speaker(s):
Nicole Bäuerle (Karlsruher Institut für Technologie (KIT))
Date:
Thursday, July 13, 2017 - 5:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We consider the problem of minimizing a certainty equivalent of the total or discounted cost over a finite time horizon which is generated by a Partially Observable Markov Decision Process (POMDP). The certainty equivalent of a random variable $X$ is defined by $U^{-1}(EU(X))$ where $U$ is an increasing function. In contrast to a risk-neutral decision maker, this optimization criterion takes the variability of the cost into account. It contains as a special case the classical risk-sensitive optimization criterion with an exponential utility.

## Contagion and Security in Inhomogeneous Financial Networks

Speaker(s):
Hamed Amini (University of Miami)
Date:
Thursday, July 13, 2017 - 4:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We derive rigorous asymptotic results for the magnitude of contagion in a large financial network and give an analytical expression for the asymptotic fraction of defaults, in terms of network characteristics. Our results extend previous studies on contagion in random graphs to inhomogeneous directed graphs with a given degree sequence and arbitrary distribution of weights. We introduce a criterion for the resilience of a large financial network to the insolvency of a small group of financial institutions and quantify how contagion amplifies small shocks to the network.

## Statistical topological data analysis: Rescaling the persistence diagram

Speaker(s):
Wolfgang Polonik (UC Davis)
Date:
Wednesday, July 12, 2017 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

A persistence diagram (PD) is one of the basic objects underlying topological data analysis. It is used to analyze topological and geometric features of an underlying space _M_, assuming availability of a random sample from _M_. Existing approaches for such analyses will be reviewed briefly, and their benefits and shortcomings will be discussed. Then we introduce ideas for rescaling PDs, which enables the derivation of novel limit theorems for the total k persistence, and other functionals of PDs.

## The Risk-Tolerance Process and the Sensitivity of Optimal Investment and Consumption

Speaker(s):
Johannes Muhle-Karbe (University of Michigan)
Date:
Thursday, June 29, 2017 - 5:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

In the perturbation analysis of various models with small frictions, a crucial role is played by the risk tolerance of the indirect utility process. Building on work of Kramkov and Sirbu, we show that this object is well defined in a general semimartingale setting. We also establish that it admits a dynamic characterisation in terms of a quadratic BSDE, which in turn allows to compute the sensitivity of optimal investment strategies and consumption plans with respect to wealth.

## Financial Asset Price Bubbles under Model Uncertainty

Speaker(s):
Francesca Biagini (LMU München)
Date:
Thursday, June 29, 2017 - 4:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We study the concept of financial bubble under model uncertainty. We suppose the agent to be endowed with a family Q of local martingale measures for the underlying discounted asset price. The priors are allowed to be mutually singular to each other. One fundamental issue is the definition of a well-posed concept of robust fundamental value of a given financial asset.

## Geometry of Log-Concave Density Estimation

Speaker(s):
Bernd Sturmfels (MPI Leipzig)
Date:
Wednesday, June 28, 2017 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We present recent work with Elina Robeva and Caroline Uhler that establishes a new link between geometric combinatorics and nonparametric statistics. It concerns shape-constrained densities on d-space that are log-concave, with focus on the maximum likelihood estimator (MLE) for weighted samples. Cule, Samworth, and Stewart showed that the logarithm of the optimal log-concave density is piecewise linear and supported on a regular subdivision of the samples. This defines a map from the space of weights to the set of regular subdivisions of the samples, i.e.

## On cross-validated lasso

Speaker(s):
Denis Chetverikov (UCLA, USA)
Date:
Wednesday, June 21, 2017 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

In this talk, we derive a rate of convergence of the Lasso estimator when the penalty parameter \lambda for the estimator is chosen using K-fold cross-validation; in particular, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of \lambda, the prediction norm of the estimation error of the cross-validated Lasso estimator is with high probability bounded from above up to a constant by (s log p/n)^{1/2} (log^{7/8}(pn)), where n is the sample size of available data, p is the number of covariates, and s is the number of non-zer

## Optimal stopping of one-dimensional diffusions with integral criteria

Speaker(s):
Carlos Oliveira (Universidade de Lisboa & HU Berlin)
Date:
Thursday, June 15, 2017 - 5:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

This work provides a full characterization of the value function and solution(s) of an optimal stopping problem for a one-dimensional diffusion with an integral criterion.
The results hold under very weak assumptions, namely, the diffusion is assumed to be a weak solution of a stochastic differential equation satisfying the Engelbert-Schmidt conditions, while the (stochastic) discount rate and the integrand are required to satisfy only general integrability conditions.

## Stochastic control under partial observation

Speaker(s):
Huyen Pham (Université Paris Diderot)
Date:
Thursday, June 15, 2017 - 4:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We study and revisit the optimal control problem of partially observed stochastic systems. By using a control randomization method, we provide a backward stochastic differential equation (BSDE) representation for the value function in a general framework including path-dependence in the coefficients (both on the state and control) and without any non degeneracy condition on the diffusion coefficient.

## Kantorovich distance based kernel for Gaussian Processes: estimation and forecast

Speaker(s):
Jean-Michel Loubes (University Toulouse)
Date:
Wednesday, June 14, 2017 - 10:00am
Location:
Hausvogteiplatz 11a, 10117 Berlin, Room 4.13 (4th floor)

Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. Here, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes.